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This paper presents a new theory of instantaneous power in single-phase circuits, which is named "ps-qs theory". The ps-qs theory is formed based on the Hilbert transform and allows us to define the active and reactive powers instantaneously in single-phase circuits that operate in transient state. In addition, a novel control strategy of active and reactive powers in single-phase circuits, which is based on the ps-qs theory, is described. Some significant characteristics of the proposed strategy are shown by experimental results.